Let x packages of nuts and y packages of bolts be produced. The objective of the manufacturer to maximize the profit is
Total Time required on machine 1 to produce x packages of nuts and y packages of bolts is equal to
Total Time required on the machine 2 to produce x packages of nuts and y packages of bolts is equal to
s
According to restrictions,
For machine 1
For machine 2
Maximize z is equal to
Subject to constraints
To solve this graphically, let us take
The lines are drawn using suitable points on the graph.
The lines intersect at P(3,3)
Now shade the region of intersection of the lines.
The feasible region is OAPB
For the corner point O(0,0), z=
For the corner point A(4,0)
For the corner point P(3,3,)
For the corner point B(0,4)
Clearly z is maximum at x=3 , y=3 and the maximum value is 10.50

2.50x + 1y
1x + 3y
3x + 1y
X + 3y ≤ 12
3x + y ≤ 12 and x,y≥0
2.50x + y
X + 3y ≤ 12
3x + y ≤ 12
X ≥ 0, y ≥ 0
X + 3y =12
3x + y = 12, x=0, y=0
O(0,0),A(4,0),P(3,3,),B(0,4)
2.5(0) +1(0)=0
2.5(4)+1(0)=10
2.5(3)+1(3)=10.5
2.5(0)+1(4)=4
